Rigorous confidence intervals for critical probabilities

2007/02/08 by Oliver Riordan, Mark Walters · 5 citations
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Probability and Statistical Research #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:05c80 #msc:60K35

paper · pdf · doi:10.1103/physreve.76.011110

published as Physical Review E 76, 011110 (2007)

arxiv created 2007/02/08 · openalex publication_date 2007/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the method of Balister, Bollobás, and Walters [Random Struct. Algorithms 26, 392 (2005)] to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases.

Citations

• The Application of Non-Crossing Partitions to Improving Percolation Threshold Bounds
• A fast Monte Carlo algorithm for site or bond percolation
• Critical percolation in finite geometries
• Bond percolation critical probability bounds for three Archimedean lattices
• Percolation

Cited by

• Percolation in networks with voids and bottlenecks
• Retention capacity of correlated surfaces
• Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions
• Universal condition for critical percolation thresholds of kagomé-like lattices
• Confidence intervals for the critical value in the divide and color model